Counting blanks in polygonal arrangements Akopyan, Arseniy ; https://orcid.org/0000-0002-2548-617X Segal Halevi, Erel Inside a two-dimensional region (``cake&quot;&quot;), there are m nonoverlapping tiles of a certain kind (``toppings&quot;&quot;). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,&quot;&quot; such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks. Society for Industrial and Applied Mathematics 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/58 Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. 2018;32(3):2242-2257. doi:<a href="https://doi.org/10.1137/16M110407X">10.1137/16M110407X</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/16M110407X info:eu-repo/semantics/altIdentifier/wos/000450810500036 info:eu-repo/semantics/altIdentifier/arxiv/1604.00960 info:eu-repo/semantics/openAccess